Wind turbine power performance measurements often occur at the perimeter of a wind farm, where the wind flow is subject to blockage effects, which might impact the measured power performance. We perform Reynolds-averaged Navier–Stokes simulations of a wind farm with five rows of 20 turbines each, operating in a conventionally neutral boundary layer, to evaluate whether the power performances measured for turbines in the upstream row would differ from that of a turbine operating in isolation under the same inflow conditions. We simulate the power performance measurements with both meteorological masts and nacelle-mounted lidars. Results show that blockage effects have an impact on the measured power performance of the wind farm turbines, with measured power coefficient varying more than 1 % relative to what is measured for the isolated turbine. In this work, we propose a method to correct for the effect of blockage on power performance measurements, yielding a curve that is more consistent with how power curves in energy yield analyses are defined and used, and thereby allowing for more useful comparisons between these curves. Our numerical results indicate that the correction method greatly reduces blockage-related variance and bias in the measured power curves. While flow modeling can be used to calculate the correction factors for actual power performance measurements in the field, we additionally show how some of the correction factors can be derived from lidar measurements. Finally, the numerical results suggest that the method could also be used to correct for the effect of wakes on power performance measurements conducted on turbines located downstream of the leading row.

Wind turbine power curve measurements play an important role in the wind industry. Manufacturers use them to better understand the performance of their fleet of operating turbines and also to refine their power predictions for new, untested designs. Wind farm owners use on-site power performance measurements to determine whether their turbines are performing at a level consistent with the predicted, theoretical power curves provided by the manufacturer. The vast majority of power performance measurements are conducted in wind farms for this purpose. Any assessment of discrepancies between actual wind farm energy production and the pre-construction estimate is not complete without verification of turbine power performance.

In an energy yield analysis, theoretical and warranted turbine power curves are the key link between the expected freestream wind resource and the predicted energy production of a planned wind farm. As such, theoretical power curves are traditionally defined as functions of hub-height freestream wind speed. When running a power performance verification test, it is straightforward to measure the power; however, the corresponding freestream wind speed – i.e., the horizontal wind speed that would prevail at the turbine location if the wind turbine was not there – is not a measurable quantity. Instead, power performance measurement campaigns are designed to measure a wind speed that has traditionally been expected to be very close to what the hub-height freestream wind speed would be if we could measure it. The IEC standard for power performance measurements

Despite these restrictions, there is growing evidence that turbine-related disturbances materially influence power performance measurements. The most compelling evidence involves field observations.

The IEC standard explains how to correct for flow distortions caused by terrain, but there is nothing on how to correct for flow disturbances/distortions caused by wind turbines. Although there is emerging recognition that turbine-induced flow disturbances should be accounted for, the wind energy community at present lacks a generally accepted method to quantify the impact of these flow disturbances and thereby correct for them. Specifically, although several models have been developed to account for blockage effects on turbine interaction loss

Here, we propose a method to correct for the impact of turbine-related disturbances on power performance measurements. The methodology, which applies to both mast- and lidar-based measurements, is designed to yield power curves that are consistent with how theoretical curves are defined. After describing the correction method in detail, including the reasoning behind it, we test the method using RANS simulations of a notional wind farm. Finally, we use virtual nacelle lidar measurements to explore whether the correction can be completed, at least partly, using nacelle lidar measurements rather than flow simulations alone.

The work is organized as follows. In Sect.

Common practice, when estimating the energy yield of a planned wind farm, is to combine the expected freestream wind resource at each turbine location with the manufacturer-provided theoretical power curve to calculate the so-called gross energy. This is the total of the energy that each turbine would produce absent the presence of the other wind turbines and other loss sources. The net energy is obtained after turbine interaction and other losses are accounted for. Thus, the power curve used in an energy yield analysis should faithfully represent the power production of the turbine as function of freestream wind speed when the turbine is operating in isolation. We refer to this power curve definition as a freestream power curve,

A power curve measured according to IEC standards,

Convert the measured curve to what would be measured if the test turbine were operating in isolation and producing the same amount of power measured in the test.

Correct for the impact of induction from the isolated turbine on the mast wind speed.

When measuring the power performance of a turbine inside a wind farm, the measured power curve

Although wind turbine power is commonly formulated as a function of freestream wind speed, it is more directly a function of the velocity across the rotor face, which, along with air density and rotor speed, determines the aerodynamic loads on the blades. In this paper, we use the average axial velocity across the rotor face as a power-equivalent wind speed,

The ratio

When

Some variations are expected for both

The numerical simulations are run using a CFD model based on STAR-CCM+, a general-purpose CFD software. The model solves the steady-state RANS equations along with a transport equation for potential temperature. The turbulence model is standard

The turbines are represented via an actuator disk model. The disk volumes are discretized with cubic mesh cells with edge lengths equal to 5 % of the rotor diameter (20 cells across the rotor diameter and 5 cells across the disk thickness). The axial and tangential body forces applied to the disk are modeled as a function of the disk-averaged axial velocity at the rotor face when the turbine is operating (

All simulations correspond to a conventionally neutral boundary layer with a thickness of approximately 1000 m. The maximum potential gradient in the capping inversion is 10 K km

We perform RANS simulations of a wind farm with five rows of 20 turbines, as shown in Fig.

Simulations are also performed with a single turbine operating within the same domain and under the same free-flow conditions of the wind farm. We simulate four different single-turbine cases in order to evaluate whether numerical effects cause different results for the isolated turbine when this is placed at different locations. We simulate the single turbine at the locations of T28, T81, T92 and T100 and, although not shown, we find that the results are independent of the location of the isolated turbine. Therefore, in the following analysis, when we refer to the case with the isolated turbine, we point at the isolated turbine at T92, as shown in Fig.

Illustrations of the wind farm layout

To test the correction method, i.e., Eqs. (

We aim to simulate five wind directions regularly distributed over the

Vertical profiles of the horizontal wind speed

The correction method is based on the combination of measurements (

We retrieve the IEC-compliant wind speed measurements with a two-beam nacelle-mounted lidar measuring at 2

Illustrations of the rotor and lidar measurement points at both 2 and 0.5

We assume horizontal homogeneity of the flow field to reconstruct the horizontal wind speed at hub height from the two-beam lidar measurements by inverting the linear system

When using lidars with more than 2 beams, i.e., the two 50-beam and the 4-beam, we neglect both the lateral and vertical components of the wind speed vector by assuming

Wind farm blockage affects the flow upstream of the wind farm, impacting the velocity relative to the flow upstream of the isolated turbine. Figure

The error bars of Fig.

Variations in wind speed

The blockage-induced velocity variations do not change much when replacing the masts with a two-beam nacelle-mounted lidar, as shown in Fig.

Similarly to the wind speed variations shown in Fig.

Since the power output is related to the velocity to the power of 3, power variations are larger in magnitude than the velocity ones, with variations from

Since

Power output against the mast-measured wind speed of all the first-row turbines for all wind directions and mast locations.

The scatter shown in Fig.

When applying Eq. (

Figure

Power output against the lidar-measured wind speed of all the first-row turbines for all wind directions.

When measuring power curves with nacelle lidars, Eq. (

Figure

Box plots of the

It should be noted that the overestimation of

We also investigate whether short-range nacelle lidar measurements can be used to replace the numerically estimated

Normalized velocity field at hub height in front of the isolated turbine

Variation of the coefficient of determination

As it can be noted in Fig.

We use the distance of

The correction method is not limited to blockage effects. In theory, it can be used to correct for any turbine-related disturbances, including wakes. Figure

When applying Eq. (

Figure

Power output against the lidar-measured wind speed of all the wind farm turbines for all wind directions.

The correction method also works well when replacing the term

Power output against the lidar-measured wind speed of all the wind farm turbines and all wind directions. Wind speed measurements are corrected with Eq. (

The short-range lidar measurements at

Scatter plots and related linear regressions between

As described in the introduction, manufacturer-issued theoretical (MIT) power curves play a central role in both energy yield analysis (EYA) and power curve verification (PCV). In energy yield analyses, MIT power curves are commonly considered functions of

How the correction methods proposed in this paper should be used depends upon the precise definition of the manufacturer-provided power curve. Of course, if one wants to use a measured power curve directly within an EYA, then the path is clear: just correct the curve using Eqs. (

Power curve correction methods for different definition of the manufacturer-issued theoretical (MIT) power curve. The power curve measurement is assumed to take place in a wind farm.

The first row in Table

Clearly, the precise definition of a MIT power curve affects how the curve should be handled. Thus, the current situation where the definition of wind speed in these curves is ambiguous should be rectified. Based on the discussions herein, the authors recommend consistently and explicitly defining the power curve in the traditional way: power as a function of hub-height freestream wind speed for the turbine operating in isolation.

Our results show that the correction method can potentially reduce both bias and uncertainty of power performance measurements. However, the approach relies on the accuracy of the flow model, which might introduce errors when applying the correction to field measurements. In addition, a large number of simulations may be required, given the potential sensitivity of

The drawbacks of relying exclusively on numerical simulations to make the corrections could be mitigated by complementing the flow model with nacelle lidar measurements. Our numerical results indicate that short-range nacelle lidar measurements can be used to reduce the impact of turbine-induced flow disturbances on power performance measurements, which improves both accuracy and precision on the derived power curve. However, when using nacelle lidar measurements together with Eq. (

During power performance tests of an isolated turbine, nacelle lidar measurements could be retrieved at both 0.5 and 2

Numerical and experimental investigations

Also, the reliability of the correction method under waked conditions could be tested by conducting power performance measurements at the wind farm edge using nacelle lidar measurements. Depending on the wind direction, the reference turbine would be either the most upwind or downwind of the farm. So,

Comparisons with field observations can help us better understand the reliability of the proposed methodology and model-predicted correction factors. Although it is not possible to validate the correction factor predictions directly, there are some common types of field observations that can be used to validate model output that is relevant to the calculations in Eqs. (

Another indirect approach to validating the correction methodology and model predictions is to apply them to measured power curves. For example, the corrections could be applied to power curve measurements on a record-by-record basis to determine whether the correction methodology reduces scatter in the measured power curve. In addition, the waked vs wake-free comparison of corrected curves described earlier in Sect.

In this work we present and evaluate a method to correct for the impact of turbine-induced flow disturbances on power performance measurements. The correction method is designed to recover the test turbine freestream power curve, i.e., a power curve that faithfully represents turbine power production as a function of freestream wind speed when it is operating in isolation. The method accounts for both the induction of the test turbine as well as the influence of surrounding turbines via blockage and sometimes wakes. Essentially, we take each wind speed value of the measured power curve and correct it to represent the freestream wind speed that would prevail if the test turbine were producing the same amount of power while operating in isolation.

Our CFD analysis suggests that the corrections can reduce uncertainty and bias in power performance measurements. Simulations of power performance measurements at a 100-turbine wind farm revealed variations in “measured”

The correction factors in this work derive from flow model output, and the same could be done when applying the methodology to real power performance measurements. That said, evidence from this study suggests that the correction factors, at least in part, could also derive from lidar measurements. Measurements taken just 0.5

Blockage effects appear to materially distort the outcome of IEC standard power performance measurements; reliable corrections to these effects would reduce uncertainty and produce curves that are more consistent with how power curves are defined and used in energy yield analyses.

The next step in this research should be to test the correction methodology on a set of real-world power performance measurements. Field observations could further clarify the validity and utility of these corrections. Additionally, it should be investigated how the method performs when CFD simulations are replaced with engineering wake models, which require lower computational costs and are more extensively used in energy yield analyses.

Code and data related to this work might be obtained by contacting the authors.

AS, JB and AP participated in the conceptualization and design of the work. AS, JB and AP participated to regular discussions on the interpretation of the results. JB theoretically defined the correction method and performed the CFD simulations. AS defined the lidar-based application of the method and conducted the post-process analysis of the CFD results, retrieving the virtual lidar measurements. AS wrote the draft manuscript. JB and AP supported the whole analysis and reviewed and edited the manuscript.

The contact author has declared that none of the authors has any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

This research has been supported by the Horizon 2020 (Lidar Knowledge Europe (LIKE), grant no. 858358).

This paper was edited by Cristina Archer and reviewed by Nicolai Gayle Nygaard and one anonymous referee.